Half-Altitude Triangle


The half-altitude triangle DeltaA^'B^'C^' of a reference triangle DeltaABC is defined by letting A^' be the midpoint between vertex A and the foot of the A-altitude on side BC, and similarly defining B^' and C^' (Kimberling 1998, pp. 172-173).

The half-altitude triangle has trilinear vertex matrix

 [1 cosC cosB; cosC 1 cosA; cosB cosA 1].

It has area


where Delta is the area of DeltaABC.

The circumcircle of the half-altitude triangle is the half-altitude circle.

See also

Half-Altitude Circle, Orthic Triangle

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Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Referenced on Wolfram|Alpha

Half-Altitude Triangle

Cite this as:

Weisstein, Eric W. "Half-Altitude Triangle." From MathWorld--A Wolfram Web Resource.

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